Question

Find the area of rectangle $BCEF$ . Round the area to the nearest whole number, if necessary.

A trapezoid A B C D is plotted on a coordinate plane. A D represents the longer base and B C represents the shorter base. Vertex A lies at ordered pair negative 5 comma 4. Vertex B lies at ordered pair 0 comma 3. Vertex C lies at ordered pair 4 comma negative 1. Vertex D lies at ordered pair 4 comma negative 5. A line is drawn from vertex B and intersects line A D at point F plotted at ordered pair negative 2 comma 1. A line is drawn from vertex C and intersects the line A D at point E plotted at ordered pair 2 comma negative 3.

The area is
square units.

Answer 1

The area of rectangle BCEF is 12 square units.

Step-by-step explanation:

To find the area of rectangle BCEF, we need to find the length and width of the rectangle. BCEF is formed by the line segment BE and the line segment CF. To find the length of BE, we subtract the x-coordinates of B and E: 0 - (-2) = 2 units. To find the length of CF, we subtract the x-coordinates of C and F: 4 - (-2) = 6 units. Therefore, the length of BCEF is 6 units and the width is 2 units. The area of a rectangle is given by the formula length × width. So, the area of rectangle BCEF is 6 × 2 = 12 square units.